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A vortex-dynamical scaling theory for flickering buoyant diffusion flames

  • Xi Xia (a1) and Peng Zhang (a1)


The flickering of buoyant diffusion flames is associated with the periodic shedding of toroidal vortices that are formed under gravity-induced shearing at the flame surface. Numerous experimental investigations have confirmed the scaling, $f\propto D^{-1/2}$ , where $f$ is the flickering frequency and $D$ is the diameter of the fuel inlet. However, the connection between the toroidal vortex dynamics and the scaling has not been clearly understood. By incorporating the finding of Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140) that the detachment of a continuously growing vortex ring is inevitable and can be dictated by a universal constant that is essentially a non-dimensional circulation of the vortex, we theoretically established the connection between the periodicity of the toroidal vortices and the flickering of a buoyant diffusion flame with small Froude number. The scaling theory for flickering frequency was validated by the existing experimental data of pool flames and jet diffusion flames.


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Albers, B. W. & Agrawal, A. K. 1999 Schlieren analysis of an oscillating gas-jet diffusion flame. Combust. Flame 119 (1–2), 8494.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Baum, H. R. & McCaffrey, B. J. 1989 Fire induced flow field-theory and experiment. Fire Safety Sci. 2, 129148.
Bejan, A. 1991 Predicting the pool fire vortex shedding frequency. Trans. ASME C: J. Heat Transfer 113 (1), 261263.
Buckmaster, J. & Peters, N. 1988 The infinite candle and its stability a paradigm for flickering diffusion flames. Symp. Intl Combust. Proc. 21 (1), 18291836.
Burke, S. P. & Schumann, T. E. W. 1928 Diffusion flames. Ind. Engng Chem. 20 (10), 9981004.
Byram, G. M. & Nelson, R. M. 1970 The modeling of pulsating fires. Fire Technol. 6 (2), 102110.
Cantwell, B., Lewis, G. & Chen, J. 1989 Topology of three-dimensional, variable density flows. In 10th Australasian Fluid Mechanics Conference, Melbourne, Australia.
Carpio, J., Sánchez-Sanz, M. & Fernández-Tarrazo, E. 2012 Pinch-off in forced and non-forced, buoyant laminar jet diffusion flames. Combust. Flame 159 (1), 161169.
Cetegen, B. M. 1997 Behavior of naturally unstable and periodically forced axisymmetric buoyant plumes of helium and helium–air mixtures. Phys. Fluids 9 (12), 37423752.
Cetegen, B. M. & Ahmed, T. A. 1993 Experiments on the periodic instability of buoyant plumes and pool fires. Combust. Flame 93 (1–2), 157184.
Chamberlin, D. S. & Rose, A. 1948 The flicker of luminous flames. Symp. Intl Combust. Proc. 1, 2732.
Chen, L. D. & Roquemore, W. M. 1986 Visualization of jet flames. Combust. Flame 66 (1), 8186.
Chen, L. D., Seaba, J. P., Roquemore, W. M. & Goss, L. P. 1989 Buoyant diffusion flames. Symp. Intl Combust. Proc. 22 (1), 677684.
Coats, C. M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22 (5), 427509.
Cox, G. 1995 Combustion Fundamentals of Fire. Academic Press.
Dabiri, J. O. & Gharib, M. 2005 Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111136.
Davis, R. W., Moore, E. F., Santoro, R. J. & Ness, J. R. 1990 Isolation of buoyancy effects in jet diffusion flame experiments. Combust. Sci. Technol. 73 (4–6), 625635.
Detriche, P. H. & Lanore, J. C. 1980 An acoustic study of pulsation characteristics of fires. Fire Technol. 16 (3), 204211.
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30 (1), 101116.
Durox, D., Yuan, T., Baillot, F. & Most, J. M. 1995 Premixed and diffusion flames in a centrifuge. Combust. Flame 102 (4), 501511.
Fang, J., Wang, J.-W., Guan, J.-F., Zhang, Y.-M. & Wang, J.-J. 2016 Momentum- and buoyancy-driven laminar methane diffusion flame shapes and radiation characteristics at sub-atmospheric pressures. Fuel 163, 295303.
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.
Ghoniem, A. F., Lakkis, I. & Soteriou, M. 1996 Numerical simulation of the dynamics of large fire plumes and the phenomenon of puffing. Symp. Intl Combust. Proc. 26 (1), 15311539.
Glezer, A. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 35323542.
Hamins, A., Yang, J. C. & Kashiwagi, T. 1992 An experimental investigation of the pulsation frequency of flames. Symp. Intl Combust. Proc. 24 (1), 16951702.
Jiang, X. & Luo, K. H. 2000 Combustion-induced buoyancy effects of an axisymmetric reactive plume. Proc. Combust. Inst. 28 (2), 19891995.
Joulain, P. 1998 The behavior of pool fires: state of the art and new insights. Symp. Intl Combust. Proc. 27 (2), 26912706.
Katta, V. R., Goss, L. P. & Roquemore, W. M. 1994 Numerical investigations of transitional H2/N2 jet diffusion flames. AIAA J. 32 (1), 8494.
Katta, V. R. & Roquemore, W. M. 1993 Role of inner and outer structures in transitional jet diffusion flame. Combust. Flame 92 (3), 274282.
Klimenko, A. Y. & Williams, F. A. 2013 On the flame length in firewhirls with strong vorticity. Combust. Flame 160, 335339.
Kolhe, P. S. & Agrawal, A. K. 2007 Role of buoyancy on instabilities and structure of transitional gas jet diffusion flames. Flow Turbul. Combust. 79 (4), 343360.
Krieg, M. & Mohseni, K. 2013 Modelling circulation, impulse, and kinetic energy of starting jets with non-zero radial velocity. J. Fluid Mech. 719, 488526.
Krueger, P., Dabiri, J. & Gharib, M. 2006 The formation number of vortex rings formed in a uniform background co-flow. J. Fluid Mech. 556, 147166.
Lawson, J. M. & Dawson, J. R. 2013 The formation of turbulent vortex rings by synthetic jets. Phys. Fluids 25 (10), 105113.
Liñán, Vera, M. & Sánchez, A. L. 2015 Ignition, liftoff, and extinction of gaseous diffusion flames. Annu. Rev. Fluid Mech. 47, 293314.
Liñán, A., Fernández-Tarrazo, E., Vera, M. & Sánchez, A. L. 2005 Lifted laminar jet diffusion flames. Combust. Sci. Technol. 177 (5–6), 933953.
Lingens, A., Neemann, K., Meyer, J. & Schreiber, M. 1996 Instability of diffusion flames. Symp. Intl Combust. Proc. 26 (1), 10531061.
Malalasekera, W. M. G., Versteeg, H. K. & Gilchrist, K. 1996 A review of research and an experimental study on the pulsation of buoyant diffusion flames and pool fires. Fire Mater. 20 (6), 261271.
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51 (1), 1532.
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81 (3), 465495.
Maxworthy, T. 1999 The flickering candle: transition to a global oscillation in a thermal plume. J. Fluid Mech. 390, 297323.
McCamy, C. S. 1956 A five-band recording spectroradiometer. J. Res. Natl Bur. Stand. 56 (5), 293299.
Mell, W. E., McGrattan, K. B. & Baum, H. R. 1996 Numerical simulation of combustion in fire plumes. Symp. Intl Combust. Proc. 26 (1), 15231530.
Mohseni, K. & Gharib, M. 1998 A model for universal time scale of vortex ring formation. Phys. Fluids 10 (10), 24362438.
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139161.
Portscht, R. 1975 Studies on characteristic fluctuations of the flame radiation emitted by fires. Combust. Sci. Technol. 10 (1–2), 7384.
Roquemore, W. M., Chen, L. D., Seaba, J. P., Tschen, P. S., Goss, L. P. & Trump, D. D. 1987 Jet diffusion flame transition to turbulence. Phys. Fluids 30 (9), 2600.
Saffman, P. G. 1978 The number of waves on unstable vortex rings. J. Fluid Mech. 84 (4), 625639.
Sato, H., Amagai, K. & Arai, M. 2000 Diffusion flames and their flickering motions related with Froude numbers under various gravity levels. Combust. Flame 123 (1), 107118.
Schönbucher, A., Arnold, B., Banhardt, V., Bieller, V., Kasper, H., Kaufmann, M., Lucas, R. & Schiess, N. 1988 Simultaneous observation of organized density structures and the visible field in pool fires. Symp. Intl Combust. Proc. 21 (1), 8392.
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24 (1), 235279.
Sibulkin, M. & Hansen, A. G. 1975 Experimental study of flame spreading over a horizontal fuel surface. Combust. Sci. Technol. 10 (1–2), 8592.
Tieszen, S. R. 2001 On the fluid mechanics of fires. Annu. Rev. Fluid Mech. 33 (1), 6792.
Tieszen, S. R., Nicolette, V. F., Gritzo, L. A., Moya, J., Holen, J. & Murray, D.1996 Vortical structures in pool fires: observation, speculation, and simulation. Tech. Rep. SAND-96-2607. Sandia National Labs., Albuquerque, NM (USA).
Trefethen, L. M. & Panton, R. L. 1990 Some unanswered questions in fluid mechanics. Appl. Mech. Rev. 43 (8), 153170.
Weckman, E. J. & Sobiesiak, A. 1989 The oscillatory behaviour of medium-scale pool fires. Symp. Intl Combust. Proc. 22 (1), 12991310.
Wu, J. Z., Ma, H. Y. & Zhou, M. D. 2007 Vorticity and Vortex Dynamics. Springer.
Xia, X. & Mohseni, K. 2015 Far-field momentum flux of high-frequency axisymmetric synthetic jets. Phys. Fluids 27 (11), 115101.
Yoshihara, N., Ito, A. & Torikai, H. 2013 Flame characteristics of small-scale pool fires under low gravity environments. Proc. Combust. Inst. 34 (2), 25992606.
Yu, D. & Zhang, P. 2017a On flame height of circulation-controlled firewhirls with variable physical properties and in power-law vortices: a mass-diffusivity-ratio model correction. Combust. Flame 182, 3647.
Yu, D. & Zhang, P. 2017b On the flame height of circulation-controlled firewhirls with variable density. Proc. Combust. Inst. 36 (2), 30973104.
Zhu, X., Xia, X. & Zhang, P. 2018 Near-field flow stability of buoyant methane/air inverse diffusion flames. Combust. Flame 191, 6675.
Zukoski, E. E., Cetegen, B. M. & Kubota, T. 1985 Visible structure of buoyant diffusion flames. Symp. Intl Combust. Proc. 20 (1), 361366.
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